Question

simplify the expression using the properties of exponents. expand any numerical portion of your answer and only include positive exponents. ((2a^{4}b)(5a^{0}b^{-1}))

Explanation:

Step1: Multiply coefficients and like bases

Multiply the coefficients \(2\) and \(5\), and use the property \(a^m \cdot a^n = a^{m + n}\) for \(a\) and \(b\) terms.
\((2a^{4}b)(5a^{0}b^{-1}) = (2\times5) \cdot a^{4 + 0} \cdot b^{1 + (-1)}\)

Step2: Simplify each part

Simplify the coefficient: \(2\times5 = 10\).
Simplify the \(a\) term: \(a^{4+0}=a^{4}\).
Simplify the \(b\) term: \(b^{1 + (-1)} = b^{0}\), and \(b^{0}=1\) (by the property \(a^0 = 1\) for \(a
eq0\)).

Combine these results: \(10\times a^{4}\times1 = 10a^{4}\)

Answer:

\(10a^{4}\)